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We explore a novel class of Yang-Baxter deformed AdS$_{4}$ $\times$ CP$^{3}$backgrounds [Jour. High Ener. Phys. \textbf{01} (2021) 056] which exhibit anon-chaotic dynamics for (super)strings those are propagating over it. Weexploit the Kovacic's algorithm to analytically study the (non-)integrabilityof the string sigma models over these deformed backgrounds. We also study thedynamics of the strings numerically where we probe the classical phase space ofthese (semi)classical strings and calculate various chaos indicators. Theseinclude studying the Poincar\'{e} sections and estimating the Lyapunovexponents. We find evidences which confirm an integrable phase space dynamicsin the (semi)classical limit. Moreover, our analytical results find perfectmatching with the numerical studies.

Non-chaotic dynamics for Yang-Baxter deformed $\text{AdS}_{4}\times \text{CP}^{3}$ superstrings